Temperature-induced spin-coherence dissipation in quantum dots

Abstract

The temperature dependence of electron-spin coherence in singly negatively charged ͑In,Ga͒As/GaAs quantum dots is studied by time-resolved Faraday rotation. The decoherence time T 2 is constant on the microsecond scale for temperatures below 15 K; for higher temperatures it shows a surprisingly sharp drop into the nanosecond range. The decrease cannot be explained through inelastic scattering with phonons, and it may be related to elastic scattering due to phonon-mediated fluctuations of the hyperfine interaction.Solid-state systems are interesting for implementation of quantum information processing because they may provide controllable qubits sufficiently protected from environmentinduced classicality. 1,2 Specifically, in semiconductor quantum dots ͑QDs͒, a qubit can be defined by the two-level system of a confined electron spin, 3 which currently attracts great attention because of its long relaxation times. The spin relaxation can be characterized by two time scales, the longitudinal relaxation time T 1 , limited by inelastic scattering, and the transverse relaxation time T 2 ͑also called decoherence time͒, for which limitations may arise also from elastic scattering. The relation between these times is nontrivial and is often summarized by the simple relationFor the T 1 time of a QD electron spin, a number of investigations exist, from both experiment and theory. Compared to higher-dimensional systems, the T 1 times are very much enhanced because the QD confinement protects the spin from the main inelastic-scattering mechanism: the electron-spin coupling with its orbital motion. In high magnetic fields, T 1 has been shown to persist over tens of milliseconds or even longer at cryogenic temperatures, 4,5 in accord with theoretical calculations. 6 Further, its dependence on external parameters such as temperature and magnetic field for neutral and charged quantum dots has been studied. [7][8][9][10] On the other hand, the information about the T 2 time is still limited. Considering that inelastic scattering would be the only channel for decoherence, T 2 may be as large as 2T 1 . However, studies at cryogenic temperatures show T 2 times in the microsecond range, showing that the elastic relaxation channel due to hyperfine interaction plays the dominant role under these conditions. 11,12 Recently, several calculations for T 2 times have been reported. [13][14][15][16][17][18][19][20][21] An important figure of merit of electron-spin qubits is stability under temperature changes. A temperature increase enhances the lattice phonon occupation, so that decoherence mechanisms involving phonons gain importance. Here we study the QD electron-spin coherence as a function of temperature. We show that coherence can be initiated by short laser pulses for temperatures up to ϳ100 K. The coherence time, however, is temperature independent only up to 15 K; above it shows a sharp drop. From model calculations we conclude that this sharp drop is not related to spin-orbit coupling but arises from hyperfine interaction fluctuatio...

Hole-spin initialization and relaxation times in InAs/GaAs quantum dots

“…The main conclusions of these studies are that in moderate magnetic fields (1-10 T) and at low temperature, the electron T e 1 and the hole T h 1 spin-relaxation times are governed by the same mechanism, i.e., the spin-orbitmediated single-phonon scattering, [4][5][6][7][8] which leads to relatively slow relaxation times in the range of milliseconds [9][10][11][12][13] with T h 1 five or ten times smaller than T e 1 . 12 However, the electron-and hole-spin coherence times T e,h 2 have been found to be in the microsecond range up to 15 K, [14][15][16][17] and for higher temperatures T e 2 has shown a sharp decrease 16 related to the modulation by phonons of the hyperfine (hf) interaction with the random fluctuating host nuclear spins.…”

Numerical analysis of optimized coherent control pulses

“…But closer inspection of the estimates for T 2 [31] reveals that the above estimate is not the relevant one. Rather the internal energy scale appears to be set by the energy splitting ∆ ≈ 70µeV of the two qubit states.…”

“…Then J ≈ 1 − 6neV ensues which implies J/B m ≈ 10 −6 − 10 −5 and α ≈ 10 4 . Hernandez et al [31] doubt the relevance of the spin relaxation via Rashba and Dresselhaus terms advocating phonon-induced dephasing [32,33]. Then one should rather estimate J 2 ≈ Γ∆ with Γ ≈ 0.2µeV implying J ≈ 4µeV.…”

“…The experimental investigation of temperature dependent spin relaxation has just started [31]. The pulses are very short (τ p ≈ 1ps) which implies for a π pulse according to B m τ p / = Θ/2 = π/2 the amplitude B m ≈ 1meV.…”

Optical initialization of hole spins inp-doped quantum dots: Orientation efficiency and loss of coherence

“…To compare it to other processes occurring in systems of this type one can use the only characteristics available, namely the total decrease of coherence and the duration of dephasing process which is equal to the laser pulse duration (here, sub-picosecond). Comparing the latter to timescales of other relevant processes occurring in discussed system, like the phonon-assisted 23,24 or hyperfine hole-nuclei coupling driven hole spin relaxation 25 , electron spin dephasing [26][27][28] or relaxation of the positive trion 29 (ranging from hundreds of picoseconds to a few microseconds), we find it to be at least three orders of magnitude shorter. This fact allows us to consider it separately and treat the dynamical spin dephasing as instantaneous on the background of the whole optical spin initialization process.…”